%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO114^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:08:36 PM UTC 2025 % Result : Theorem 3.91s 4.11s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.11 % Problem : SYO114^5 : TPTP v9.2.0. Released v4.0.0. % 0.02/0.12 % Command : duper %s % 0.12/0.31 % Computer : n006.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Fri Oct 3 13:27:53 EDT 2025 % 0.12/0.31 % CPUTime : % 3.91/4.11 SZS status Theorem for theBenchmark.p % 3.91/4.11 SZS output start Proof for theBenchmark.p % 3.91/4.11 Clause #0 (by assumption #[]): Eq % 3.91/4.11 (Not % 3.91/4.11 (Not % 3.91/4.11 (And % 3.91/4.11 (And (∀ (Xz : Iota), And (Or (cP Xz) (cR Xz)) (cQ Xz)) % 3.91/4.11 (∀ (Xx : Iota), % 3.91/4.11 Exists fun Xy => Or (Or (Or (Or (cP Xx) (Not (cQ Xx))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d)))) % 3.91/4.11 (Or (Not (cP a)) (Not (cP b)))))) % 3.91/4.11 True % 3.91/4.11 Clause #1 (by clausification #[0]): Eq % 3.91/4.11 (Not % 3.91/4.11 (And % 3.91/4.11 (And (∀ (Xz : Iota), And (Or (cP Xz) (cR Xz)) (cQ Xz)) % 3.91/4.11 (∀ (Xx : Iota), % 3.91/4.11 Exists fun Xy => Or (Or (Or (Or (cP Xx) (Not (cQ Xx))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d)))) % 3.91/4.11 (Or (Not (cP a)) (Not (cP b))))) % 3.91/4.11 False % 3.91/4.11 Clause #2 (by clausification #[1]): Eq % 3.91/4.11 (And % 3.91/4.11 (And (∀ (Xz : Iota), And (Or (cP Xz) (cR Xz)) (cQ Xz)) % 3.91/4.11 (∀ (Xx : Iota), Exists fun Xy => Or (Or (Or (Or (cP Xx) (Not (cQ Xx))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d)))) % 3.91/4.11 (Or (Not (cP a)) (Not (cP b)))) % 3.91/4.11 True % 3.91/4.11 Clause #3 (by clausification #[2]): Eq (Or (Not (cP a)) (Not (cP b))) True % 3.91/4.11 Clause #4 (by clausification #[2]): Eq % 3.91/4.11 (And (∀ (Xz : Iota), And (Or (cP Xz) (cR Xz)) (cQ Xz)) % 3.91/4.11 (∀ (Xx : Iota), Exists fun Xy => Or (Or (Or (Or (cP Xx) (Not (cQ Xx))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d)))) % 3.91/4.11 True % 3.91/4.11 Clause #5 (by clausification #[3]): Or (Eq (Not (cP a)) True) (Eq (Not (cP b)) True) % 3.91/4.11 Clause #6 (by clausification #[5]): Or (Eq (Not (cP b)) True) (Eq (cP a) False) % 3.91/4.11 Clause #7 (by clausification #[6]): Or (Eq (cP a) False) (Eq (cP b) False) % 3.91/4.11 Clause #8 (by clausification #[4]): Eq (∀ (Xx : Iota), Exists fun Xy => Or (Or (Or (Or (cP Xx) (Not (cQ Xx))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d))) % 3.91/4.11 True % 3.91/4.11 Clause #9 (by clausification #[4]): Eq (∀ (Xz : Iota), And (Or (cP Xz) (cR Xz)) (cQ Xz)) True % 3.91/4.11 Clause #10 (by clausification #[8]): ∀ (a : Iota), Eq (Exists fun Xy => Or (Or (Or (Or (cP a) (Not (cQ a))) (Not (cQ Xy))) (Not (cQ c))) (Not (cQ d))) True % 3.91/4.11 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (Or (Or (Or (Or (cP a) (Not (cQ a))) (Not (cQ (skS.0 0 a a_1)))) (Not (cQ c))) (Not (cQ d))) True % 3.91/4.11 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (Or (Or (Or (cP a) (Not (cQ a))) (Not (cQ (skS.0 0 a a_1)))) (Not (cQ c))) True) (Eq (Not (cQ d)) True) % 3.91/4.11 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (Not (cQ d)) True) % 3.91/4.11 (Or (Eq (Or (Or (cP a) (Not (cQ a))) (Not (cQ (skS.0 0 a a_1)))) True) (Eq (Not (cQ c)) True)) % 3.91/4.11 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (Or (Or (cP a) (Not (cQ a))) (Not (cQ (skS.0 0 a a_1)))) True) (Or (Eq (Not (cQ c)) True) (Eq (cQ d) False)) % 3.91/4.11 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (Not (cQ c)) True) % 3.91/4.11 (Or (Eq (cQ d) False) (Or (Eq (Or (cP a) (Not (cQ a))) True) (Eq (Not (cQ (skS.0 0 a a_1))) True))) % 3.91/4.11 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (cQ d) False) % 3.91/4.11 (Or (Eq (Or (cP a) (Not (cQ a))) True) (Or (Eq (Not (cQ (skS.0 0 a a_1))) True) (Eq (cQ c) False))) % 3.91/4.11 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (cQ d) False) % 3.91/4.11 (Or (Eq (Not (cQ (skS.0 0 a a_1))) True) (Or (Eq (cQ c) False) (Or (Eq (cP a) True) (Eq (Not (cQ a)) True)))) % 3.91/4.11 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (cQ d) False) % 3.91/4.11 (Or (Eq (cQ c) False) (Or (Eq (cP a) True) (Or (Eq (Not (cQ a)) True) (Eq (cQ (skS.0 0 a a_1)) False)))) % 3.91/4.11 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq (cQ d) False) % 3.91/4.11 (Or (Eq (cQ c) False) (Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq (cQ a) False)))) % 3.91/4.11 Clause #20 (by clausification #[9]): ∀ (a : Iota), Eq (And (Or (cP a) (cR a)) (cQ a)) True % 3.91/4.11 Clause #21 (by clausification #[20]): ∀ (a : Iota), Eq (cQ a) True % 3.91/4.11 Clause #23 (by backward demodulation #[21, 19]): ∀ (a a_1 : Iota), % 3.91/4.11 Or (Eq True False) (Or (Eq (cQ c) False) (Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq (cQ a) False)))) % 3.91/4.11 Clause #28 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (cQ c) False) (Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq (cQ a) False))) % 3.91/4.11 Clause #29 (by forward demodulation #[28, 21]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq (cQ a) False))) % 3.91/4.12 Clause #30 (by clausification #[29]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq (cQ a) False)) % 3.91/4.12 Clause #31 (by forward demodulation #[30, 21]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Or (Eq (cQ (skS.0 0 a a_1)) False) (Eq True False)) % 3.91/4.12 Clause #32 (by clausification #[31]): ∀ (a a_1 : Iota), Or (Eq (cP a) True) (Eq (cQ (skS.0 0 a a_1)) False) % 3.91/4.12 Clause #33 (by superposition #[32, 21]): ∀ (a : Iota), Or (Eq (cP a) True) (Eq False True) % 3.91/4.12 Clause #34 (by clausification #[33]): ∀ (a : Iota), Eq (cP a) True % 3.91/4.12 Clause #35 (by backward demodulation #[34, 7]): Or (Eq True False) (Eq (cP b) False) % 3.91/4.12 Clause #40 (by clausification #[35]): Eq (cP b) False % 3.91/4.12 Clause #41 (by superposition #[40, 34]): Eq False True % 3.91/4.12 Clause #42 (by clausification #[41]): False % 3.91/4.12 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------